Ernst Steinitz
Encyclopedia
Ernst Steinitz was a German
mathematician
.
), Silesia
, Germany
(now in Poland
), the son of Sigismund Steinitz, a Jewish coal merchant, and his wife Auguste Cohen; he had two brothers. He studied at the University of Breslau and the University of Berlin, receiving his Ph.D. from Breslau in 1894. Subsequently, he took positions at Charlottenberg (now the Technical University of Berlin
), Breslau, and the University of Kiel
, Germany, where he died in 1928. Steinitz married Martha Steinitz and had one son.
of three lines per point and three points per line could be realized as a configuration of straight lines in the Euclidean plane with the possible exception of one of the lines. His thesis also contains the
proof of König's theorem
for regular bipartite graphs, phrased in the language of configurations.
In 1910 Steinitz published the very influential paper Algebraische Theorie der Körper (German
: Algebraic Theory of Fields, Crelle's Journal
(1910), 167–309). In this paper he axiomatically studies the properties of fields
and defines important concepts like prime field, perfect field
and the transcendence degree
of a field extension
. Steinitz proved that every field has an algebraic closure
. He also made fundamental contributions to the theory of polyhedra: Steinitz's theorem
for polyhedra is that the 1-skeletons of convex polyhedra are exactly the 3-connected planar graph
s. His work in this area was published posthumously as a 1934 book, Vorlesungen über die Theorie der Polyeder unter Einschluss der Elemente der Topologie, by Hans Rademacher
.
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Biography
Steinitz was born in Laurahütte (Siemianowice ŚląskieSiemianowice Slaskie
Siemianowice Śląskie aka Siemianowice ; is a city in Upper Silesia in southern Poland, near Katowice. The central district of the Upper Silesian Metropolitan Union - metropolis with the population of 2 millions...
), Silesia
Silesia
Silesia is a historical region of Central Europe located mostly in Poland, with smaller parts also in the Czech Republic, and Germany.Silesia is rich in mineral and natural resources, and includes several important industrial areas. Silesia's largest city and historical capital is Wrocław...
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
(now in Poland
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
), the son of Sigismund Steinitz, a Jewish coal merchant, and his wife Auguste Cohen; he had two brothers. He studied at the University of Breslau and the University of Berlin, receiving his Ph.D. from Breslau in 1894. Subsequently, he took positions at Charlottenberg (now the Technical University of Berlin
Technical University of Berlin
The Technische Universität Berlin is a research university located in Berlin, Germany. Translating the name into English is discouraged by the university, however paraphrasing as Berlin Institute of Technology is recommended by the university if necessary .The TU Berlin was founded...
), Breslau, and the University of Kiel
University of Kiel
The University of Kiel is a university in the city of Kiel, Germany. It was founded in 1665 as the Academia Holsatorum Chiloniensis by Christian Albert, Duke of Holstein-Gottorp and has approximately 23,000 students today...
, Germany, where he died in 1928. Steinitz married Martha Steinitz and had one son.
Mathematical works
Steinitz's 1894 thesis was on the subject of projective configurations; it contained the result that any abstract description of an incidence structureIncidence structure
In mathematics, an incidence structure is a tripleC=.\,where P is a set of "points", L is a set of "lines" and I \subseteq P \times L is the incidence relation. The elements of I are called flags. If \in I,...
of three lines per point and three points per line could be realized as a configuration of straight lines in the Euclidean plane with the possible exception of one of the lines. His thesis also contains the
proof of König's theorem
König's theorem (graph theory)
In the mathematical area of graph theory, König's theorem, proved by Dénes Kőnig in 1931, describes an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs...
for regular bipartite graphs, phrased in the language of configurations.
In 1910 Steinitz published the very influential paper Algebraische Theorie der Körper (German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
: Algebraic Theory of Fields, Crelle's Journal
Crelle's Journal
Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik .- History :...
(1910), 167–309). In this paper he axiomatically studies the properties of fields
Field (mathematics)
In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms...
and defines important concepts like prime field, perfect field
Perfect field
In algebra, a field k is said to be perfect if any one of the following equivalent conditions holds:* Every irreducible polynomial over k has distinct roots.* Every polynomial over k is separable.* Every finite extension of k is separable...
and the transcendence degree
Transcendence degree
In abstract algebra, the transcendence degree of a field extension L /K is a certain rather coarse measure of the "size" of the extension...
of a field extension
Field extension
In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties...
. Steinitz proved that every field has an algebraic closure
Algebraic closure
In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics....
. He also made fundamental contributions to the theory of polyhedra: Steinitz's theorem
Steinitz's theorem
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the 3-vertex-connected planar graphs...
for polyhedra is that the 1-skeletons of convex polyhedra are exactly the 3-connected planar graph
Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints...
s. His work in this area was published posthumously as a 1934 book, Vorlesungen über die Theorie der Polyeder unter Einschluss der Elemente der Topologie, by Hans Rademacher
Hans Rademacher
Hans Adolph Rademacher was a German mathematician, known for work in mathematical analysis and number theory.-Biography:...
.